The speed of the alpha particle is approximately 2.18 x 10^7 m/s.
The speed of the alpha particle can be determined using the formula for the centripetal force experienced by a charged particle moving in a magnetic field. The centripetal force (Fc) is given by the equation Fc = (q * B * v) / r, where q is the charge of the particle, B is the magnetic field strength, v is the speed of the particle, and r is the radius of the circular path.
In this case, the charge of the alpha particle (q) is +2e, where e is the elementary charge (approximately 1.602 x 10^-19 C). Substituting the given values of q = +2e, B = 1.20 T, and r = 0.045 m into the formula, we can solve for the speed (v).
Using the rearranged formula v = (r * Fc) / (q * B), and recognizing that Fc is the centripetal force required for circular motion, we can express it as m * a, where m is the mass of the alpha particle and a is the centripetal acceleration. The mass of the alpha particle is 4.00 u, and 1 u = 1.661 x 10^-27 kg.
After calculating the centripetal acceleration, the speed of the alpha particle is found to be approximately 2.18 x 10^7 m/s, ensuring that the particle moves in a circular path of the given radius under the influence of the specified magnetic field.